Traumatic Systolic Blood Pressure Modeling: A Spectral Gaussian Process Regression Approach with Robust Sample Covariates

Abstract

Physiological vital signs acquired during traumatic events are informative on the dynamics of the trauma and their relationship with other features such as sample-specific covariates. Non-time dependent covariates may introduce extra challenges in the Gaussian Process (<img src=image/13425527_01.gif>) regression, as their main predictors are functions of time. In this regard, the paper introduces the use of Orthogonalized Gnanadesikan-Kettering covariates for handling such predictors within the Gaussian process regression framework. Spectral Bayesian <img src=image/13425527_01.gif> regression is usually based on symmetric spectral frequencies and this may be too restrictive in some applications, especially physiological vital signs modeling. This paper builds on a fast non-standard variational Bayes method using a modified Van der Waerden sparse spectral approximation that allows uncertainty in covariance function hyperparameters to be handled in a standard way. This allows easy extension of Bayesian methods to complex models where non-time dependent predictors are available and the relationship between the smoothness of trend and covariates is of interest. The utility of the methods is illustrated using both simulations and real traumatic systolic blood pressure time series data.